Chromatography is an increasingly important separation technique in the fine chemical, pharmaceutical and biotechnological industries. The development of accurate, reliable mathematical models for chromatography is necessary for an efficient optimisation of the process. The past decade has seen a tremendous advance in the mathematical modelling and optimisation of the chromatographic processes, with the increase in computational power that is now available. The purposes of this work are to (1) compare chromatographic models, (2) examine the choice of chromatographic models employed and (3) compare different chromatography configurations applied to the same process. With the variety of chromatography models available, there is a need to decide which model is best suited to a given process and the means by which the model parameters can be determined. A novel approach is proposed in this thesis for the model parameter and model selection for chromatographic processes to address both these issues and is illustrated using three case studies. This work highlights the differences in using simulated, theoretical data (which most modelling work commonly illustrated with) and experimental data, particularly data of complex bio-mixtures. Model selection is conducted using a recent graphical interpretation method, discussing the advantages and disadvantages of this method. Over the years, the operation of the chromatographic process in these industries has undergone some changes and it is no longer limited to batch processing. Whilst the single column is still popular in preparative chromatography, multi-column processes are now becoming increasingly popular in industrial-scale chromatography to produce large amounts of highly purified products. In light of the diversity of operational policies now available to chromatography, the second half of this thesis addresses examines the differences between the single column and the multicolumn chromatographic processes. Preliminary work is done on developing a detailed model of the simulated moving bed (SMB) chromatographic process, presenting both a dynamic model and two cyclic steady state (CSS) models. A theoretical case study is then optimised for the operation of the SMB process. The simulated moving bed (SMB) process and its recent variation, the Varicol process, are particularly well known. Such processes are continuous and are able to produce large quantities of high purified products. The decision of choosing either a single column or multi-column process for a separation is not a clear cut one. As the configurations and process operations in these processes are vastly different, an economic comparison between the optimised process alternatives is thus necessary to properly assess the strengths and weaknesses of each system, particularly from an industrial point of view. In column chromatography, a single column, as well as a single column with recycle and peak shaving operations, are considered, whilst for the multi-column alternative, the SMB process and its variations (Varicol, Powerfeed etc.) are examined.